Lect1_hbari - Lecture 1: Demystifying h and i We are often...

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Lecture 1: Demystifying h and i •We are often told that the presence of h distinguishes quantum from classical theories. •One of the striking features of Schrödinger's equation is the fact that the variable, Ψ , is complex, whereas classical theories deal with real variables QM: CM: d dt x ( t ) = p H ( x , p ) d dt p ( t ) = x H ( x , p ) d dt v E ( v r , t ) = 1 c 2 v × v B ( v r , t ) d dt v B ( v r , t ) = v × v E ( v r , t )
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•Q: Is h necessary at all? •By changing units we can of course make h disappear from QM •But if it is truly fundamental, shouldn’t this same choice of units make h appear then in CM? •If system has natural length scale and energy scale, then h is needed to relate then to the natural mass scale. i t ψ ( ρ , t ) = 1 2 m 0 m 2 ∂ρ 2 ( , t ) + u ( ) ( , t )
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•Same mass scale makes CM dimensionless as
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Lect1_hbari - Lecture 1: Demystifying h and i We are often...

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